Question

Tick (✓) the correct answer:
In a regular polygon, each interior angle is thrice the exterior angle. The number os sides of the polygon is
(a) 6
(b) 8
(c) 10
(d) 12

Answer 1

(b) 8
For a regular polygon with n sides:
Each exterior angle = $\frac{360}{n}$
Each interior angle = $180-\frac{360}{n}$

$$\begin{gathered} \therefore 180-\frac{360}{n}=3\left(\frac{360}{n}\right) \\ \Rightarrow 180=4\left(\frac{360}{n}\right) \\ \Rightarrow n=\frac{4\times 360}{180}=8 \end{gathered}$$